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#1 is easy and very clear.
Rule 4-2-2d: The ball becomes dead when any legal free kick or scrimmage kick which is not a scoring attempt or which is a grounded scoring attempt, breaks the plane of R's goal line.
Rule 4-2-2f: The ball becomes dead when the kickers catch or recover any free kick anywhere and when the kickers catch or recover a scrimmage kick beyond the neutral zone.
Rule 6-3-1a: It is a touchback if any free kick or scrimmage kick which is not a scoring attempt or which is a grounded three point field goal attempt, breaks the plane of R's goal line.
It is irrelevant where K's feet are when he gains possession of the ball. The ball is dead where he gained possession. 1st and goal inside the 1 for R (since placing the nose of the ball at the 1 would put the back of the ball on the goal line, you move the ball forward slightly so it's not in the end zone).
The second one could be a little trickier because there are several rules at play.
Rule 1-2-4: ....When properly placed, the goal line pylon is out of bounds at the intersection of the sideline and the goal line extended.
Rule 2-28-1: A player or other person is out of bounds when any part of the person is touching anything, other than player or game official, who is on our outside the sideline or end line.
Rule 2-28-3: A loose ball is out of bounds when it touches anything, including a player or game official, who is out of bounds.
Rule 4-3-1: When a loose ball goes out of bounds, the out-of-bounds spot is fixed by the har line where the foremost point of the ball crossed the sideline.
If you use these rules, you could infer that if the ball hit the FRONT of the pylon, it had to cross the sideline before it was technically out of bounds so the inbounds spot would be at that point. If the ball hit the INSIDE of the pylon, it is just now crossing the sideline and since the pylon is lined up with the goal line, it would be a touchback (you could construct similar situations using the outside, back and top of the pylon). So it could be interpreted that it depends on which side of the pylon the ball hits.
Then if you read Rule 4-3-2, it clears the situation pretty well.
"...If the ball touches a pylon, it is out of bounds behind the goal line."
So in your situation #2, it's a touchback.
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